Final answer:
The domain of a function is the set of all real numbers that will output real values when inserted into the function. When two functions are composed, the resultant domain is governed by the 'inside' function and the function resulting from the composition. Therefore, the domain of the composite function (m o n)(x) = m(n(x)) = m(x-3) is the same as the domain of n(x), which is all real numbers.
Step-by-step explanation:
In mathematics, the domain of a function is the set of all possible input values (often called 'x' values) that will output real number values when substituted into the function. The given functions are m(x)=(x+5)/(x-1) which is a rational function, and n(x)=x-3 which is a linear function.
For m(x), the function is undefined when x=1 as it would result in a division by zero. Therefore, the domain of m(x) is all real numbers except 1. For n(x), the function is defined for all real numbers, thus, its domain is all real numbers.
Whenever we have composite functions, we must consider the domain of the inside function and the domain after applying the outside function. Here, the composite function is (m o n)(x) = m(n(x)) = m(x-3). Incidentally, substituting 'x-3' into 'm' does not ever make the denominator equal zero. Thus, the domain of (m o n)(x) is same as domain of n(x), all real numbers.
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